$tail ='L'$: The lower tail probability is returned, that is $P (G \leq g : α, β)$ .
$tail ='U'$: The upper tail probability is returned, that is $P (G \geq g : α, β)$ .

Constraint:

tail ='L'

'U'

2: $g$ – Real (Kind=nag_wp) Input

On entry:

g

, the value of the gamma variate.

Constraint:

g \geq 0.0

3: $a$ – Real (Kind=nag_wp) Input

On entry: the parameter

α

of the gamma distribution.

Constraint:

a > 0.0

4: $b$ – Real (Kind=nag_wp) Input

On entry: the parameter

β

of the gamma distribution.

Constraint:

b > 0.0

5: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

−1

1

to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of

0

causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of

−1

means that an error message is printed while a value of

1

means that it is not.

If halting is not appropriate, the value

−1

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

ifail = 1

2

3

4

on exit, then g01eff returns

0.0

$ifail = 1$: On entry, $tail = ⟨ value ⟩$ .
Constraint: $tail ='L'$ or $'U'$ .

$ifail = 2$: On entry, $g = ⟨ value ⟩$ .
Constraint: $g \geq 0.0$ .

$ifail = 3$: On entry, $a = ⟨ value ⟩$ and $b = ⟨ value ⟩$ .
Constraint: $a > 0.0$ and $b > 0.0$ .

$ifail = 4$: The algorithm has failed to converge in $⟨ value ⟩$ iterations. The probability returned should be a reasonable approximation to the solution.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The result should have a relative accuracy of machine precision. There are rare occasions when the relative accuracy attained is somewhat less than machine precision but the error should not exceed more than

1

2

decimal places. Note also that there is a limit of

18

decimal places on the achievable accuracy, because constants in s14baf are given to this precision.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

g01eff is not threaded in any implementation.

9 Further Comments

The time taken by g01eff varies slightly with the input arguments g, a and b.

10 Example

This example reads in values from a number of gamma distributions and computes the associated lower tail probabilities.

g01ef: FL CL CPP AD PY MB

NAG FL Interfaceg01eff (prob_​gamma)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g01eff (prob_gamma)